Pattern Center and Distortion Determined from Faint, Diffuse Electron Diffraction Rings from Amorphous Materials.

Diffuse rings from amorphous materials sit on a steep background resulting in a monotonically decreasing intensity over scattering vector length, frequently with no clear local maximum that could be used to determine the center of the ring. The novelty of the method reported here is that it successful processes such weak patterns. It is based on separating the angular dependence of the positions of the maxima on the azimuthal angle in the measured two-dimensional pattern for a manually preselected peak. Both pattern center and elliptical distortion are simultaneously refined from this angular dependence. Both steps are based on nonlinear least square fitting, using the Levenberg-Marquardt method. It can be successfully applied to any amorphous patterns provided they were recorded with experimental conditions that facilitate dividing them into sectors with acceptable statistics. Patterns with the center shifted to the camera corner (recording a quadrant of a ring) can also be reliably evaluated, keeping precalibrated values of the elliptical distortion fixed during the fit. Finally, the limited number of counts in any pattern is overcome by cumulating many patterns (from equivalent areas) into a single pattern. Eliminating false effects is facilitated by masking out unwanted parts of any recorded pattern from processing.